3 problems

The conjecture. The same right asymptotic order should hold for $r=1$:

Let $d\in\mathbb{N}$, let $\mathbb{T}^d$ be the $d$-dimensional torus, and let $\boldsymbol{W}^r_p(\mathbb{T}^d)$ and $\boldsymbol{H}^r_p(\mathbb{T}^d)$ denote the mixed Sobolev an…

Let $\varrho_m(\mathbf W^r_p,L_p)$ denote the optimal sampling-recovery error from the Sobolev class $\mathbf W^r_p$ in the $L_p$ norm, using $m$ samples. Diagonal Sobolev sampling…